Bayesian Model Selection in Nonlinear Subspace Identification

In nonlinear system identification, one of the main challenges is how to select a nonlinear model. The accuracy of nonlinear subspace identification depends on the accuracy of the nonlinear feedback force that the user chooses. Considering the uncertainties in the selection process of an appropriate nonlinear model, a novel Bayesian probability method calculation framework based on response data is established to improve the accuracy of nonlinear subspace identification. Three implementation steps are introduced: 1) establish the candidate model database; 2) the reconstructed signal can be calculated by nonlinear subspace identification; and 3) the posterior probability of each candidate model is estimated to get the optimal nonlinear model and determine the nonlinear coefficients of the nonlinearities. Two numerical simulations are investigated: a two-degree-of-freedom spring-mass system with nonlinear damping and a cantilever beam with nonlinear stiffness. The influence of the noise on the robustness of the algorithm is considered. The experimental investigation is eventually undertaken considering a device showing elastic and damping nonlinearities. The latter is represented by a friction model depending on both velocity and displacement. Results indicate that the proposed approach can effectively identify the nonlinear system behavior with high accuracy.